Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in PYTHON3):

Solution:

N = int(input())
P = list(map(int,input().split()))
P2 =[0]*(N+1)

i = N-1
T = 0

for j in range(N):
    P2[P[j]] = j+1

while i >= 0:
    if P2[i] > P2[i+1]:
        T = 1
        f = i+1
        i = i-1
        break
    i = i-1
    

while i > 0:
    if (P2[i+1]-P2[i])*(P2[i]-P2[f])*(P2[f]-P2[i+1]) > 0:
        T = T+1
        f = i+1
    i = i-1

print(T)